Let S be the set of all real numbers and T be the set of all positive real numbers. Find a one to one mapping f of S onto T such that f (s1, + s2) = f(s1)f(s2) for all s1,s2 are elements of S.

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Q: Consider the functions f : A → B, g : B → A and h : B → A such that if gf = 1 Ą and fh = 1B. Prove…

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A: we know that  gof is Bijective,  hence, gof has one to one correspondence,  This deduces that g must…

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Q: Let f(x) = (x + 1)² - 1, x 2-1. Then the set {x:f(x) = f(x)} is

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Q: Determine whether each of these functions from R to R is a bijection.  f(x)=2x+4

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Q: Show that the real-valued function f: R → R defined by f(x) = x° x E R. 3x2 + 3x + 1 increases for…

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A: This question related to function and bijection.

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A: For onto from set A to B, Every value of set B should exist atleast once in the function.

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A: Given that:  f : A → B, f(a) = 3, f(b) = 4, f(c) = 2, f(d) = 5, f(e) = 1.   Since, the images (i.e.…

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Q: Suppose that a function ƒ(x) has the property that ƒ(x1 x2) = ƒ(x1) + ƒ(x2) for any two positive…

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Q: Is the set {(-3,0,3),(1,-1,2)(4,-2,2), (2,1,3)} of R' linear dependent over R?

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Q: Let R be the set of all real numbers. Determine every function g: R→ R such that for all real…

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A: Given.